Finite Group Databasebeta

← #34057678

Subgroups — #34057678

Order 19072.

360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750349C211yesmaximal, characteristic, complemented
2#23750345C211yesmaximal, characteristic, complemented
3#23750006C212yesmaximal
4#23750004C211yesmaximal, characteristic, complemented
5#23749850C212yesmaximal, complemented
6#23749845C212yesmaximal, complemented
7#23749831C211yesmaximal, characteristic, complemented
8#23749749C211yesmaximal, characteristic, complemented
9#23749717C212yesmaximal, complemented
10C4×#14558721C211yesmaximal, characteristic
11#461×C149C211yesmaximal, characteristic, complemented
12C2×#14558726C2212yes—
13C2×#14558726C2212yes—
14C2×#14558725C2212yes—
15C2×#14558721C2211yescharacteristic
16#18011911C2211yescharacteristic
17#18011906—22no—
18#18011904—22no—
19#18011900C2212yes—
20#18011898C2212yes—
21#18011891—21no—
22#18011890—21no—
23Q8×Dic149C2212yes—
24C4×Dic298C2211yescharacteristic
25#18011876C2212yes—
26C4×D596C2211yescharacteristic
27#18011870—21no—
28#18011869—21no—
29#18011844C2211yescharacteristic
30#18011840C2212yes—
31#18011836C2212yes—
32#18011832C2211yescharacteristic
33#18011831C2211yescharacteristic
34C4×#11924746C2211yescharacteristic
35C8×Dic149C2212yes—
36C2×SD16×C149C2212yes—
37C4⋊Q8×C149C2211yescharacteristic
38C4×D4×C149C2211yescharacteristic
39C4⋊C8×C149C2211yescharacteristic
40#103×C149C2212yes—
41C2×Dic298D411yescharacteristic
42C2×Dic298C2312yes—
43C2×D596C2311yescharacteristic
44C2×C4×D149—21no—
45#14558726—24no—
46#14558726—42no—
47#14558725—42no—
48#14558721—22no—
49C2×#11924746C2311yescharacteristic
50C2×#11924746C2311yescharacteristic
51C4⋊Dic149—22no—
52C4⋊Dic149—21no—
53C4⋊Dic149—21no—
54C4⋊Dic149D411yescharacteristic
55C4⋊Dic149C2311yescharacteristic
56#14558715—22no—
57#14558715D412yes—
58C22⋊Dic149—22no—
59C22⋊Dic149—22no—
60#14558713—22no—
61#14558713—22no—
62#14558713—21no—
63C4×Dic149—22no—
64C4×Dic149—22no—
65C4×Dic149C2312yes—
66C2×Q8×C149C2312yes—
67C2×D4×C149C2311yescharacteristic
68C22×C4×C149—21no—
69SD16×C149—42no—
70C2×C8×C149C2312yes—
71C4⋊C4×C149—21no—
72C4⋊C4×C149—21no—
73C4⋊C4×C149C2311yescharacteristic
74C22⋊C4×C149—21no—
75C42×C149C2311yescharacteristic
76C22×D149—21no—
77Dic298—22no—
78Dic298—22no—
79Dic298—22no—
80D596—21no—
81D596—21no—
82C2×Dic149—21no—
83C2×Dic149—22no—
84C2×Dic149C2×D412yes—
85C2×Dic149C2×D412yes—
86C4×D149—42no—
87#11924746—21no—
88#11924746#4112yes—
89C23×C149—21no—
90Q8×C149—22no—
91Q8×C149—22no—
92D4×C149—21no—
93D4×C149—21no—
94C2×C4×C149—21no—
95C2×C4×C149—22no—
96C2×C4×C149—42no—
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2411yescharacteristic
100C8×C149—22no—
101C22×C149—41no—
102C22×C149—41no—
103C22×C149—41no—
104C22×C149C22×D411yescharacteristic
105C2×D149—41no—
106C2×D149—41no—
107C2×D149—41no—
108C4×C149—21no—
109C4×C149—42no—
110C4×C149—41no—
111C4×C149#13512yes—
112C4×C149C2×#4111yescharacteristic
113C4×C149H(5,𝔽2)11yescharacteristic
114Dic149—22no—
115Dic149—22no—
116Dic149—42no—
117Dic149—41no—
118C2×C149—81no—
119C2×C149#55011yescharacteristic
120C2×C149C2×#13511yescharacteristic
121C2×C149#57811yescharacteristic
122D149—81no—
123C149#339311yescharacteristic, complemented, Sylow
124#3393—1491nomaximal, Sylow
125#556—1491no—
126#556—1491no—
127#495—1492no—
128#494—1491no—
129#464—1492no—
130#464—1492no—
131#461—1491no—
132#461D14911yescharacteristic, complemented
133C8×Q8—1491no—
134C4×Q16—1492no—
135C4×D8—1491no—
136C2×Q16—1492no—
137C2×Q16—1492no—
138C2×SD16—1492no—
139C2×SD16C2×D14912yes—
140C2×D8—1491no—
141C4⋊Q8—1491no—
142C4⋊Q8C2×D14911yescharacteristic
143#126—2982no—
144#126—2982no—
145#124—1492no—
146#124—1492no—
147C22⋊Q8—2981no—
148C22⋊Q8—2981no—
149C4×Q8—1492no—
150C4×Q8—1492no—
151C4×Q8—1491no—
152C4×D4—1491no—
153C4×D4C2×D14911yescharacteristic
154#117—2981no—
155#117—2981no—
156#107—1491no—
157C4⋊C8—1492no—
158C4⋊C8C2×D14911yescharacteristic
159#103—1492no—
160#103C2×D14912yes—
161#102—1491no—
162#102—1491no—
163C4×C8—1492no—
164C4×C8—1491no—
165C2×Q8—1492no—
166C2×Q8—1491no—
167C2×Q8C22×D14912yes—
168C2×D4—1491no—
169C2×D4C22×D14911yescharacteristic
170C22×C4—21no—
171C22×C4—2981no—
172Q16—2984no—
173Q16—5962no—
174SD16—42no—
175SD16—5962no—
176D8—2982no—
177C2×C8—1491no—
178C2×C8—1491no—
179C2×C8C22×D14912yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—2982no—
183C4⋊C4—2982no—
184C4⋊C4—2981no—
185C4⋊C4—2981no—
186C4⋊C4—1491no—
187C4⋊C4—1491no—
188C4⋊C4—1492no—
189C4⋊C4C22×D14911yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—2982no—
192C22⋊C4—2982no—
193C22⋊C4—2982no—
194C22⋊C4—2982no—
195C22⋊C4—2981no—
196C42—2982no—
197C42—2982no—
198C42—1492no—
199C42C22×D14911yescharacteristic
200C23—21no—
201C23—2981no—
202Q8—22no—
203Q8—22no—
204Q8—2982no—
205Q8—2982no—
206Q8—2982no—
207D4—21no—
208D4—21no—
209D4—2981no—
210D4—2981no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—2981no—
215C2×C4—2982no—
216C2×C4—5962no—
217C2×C4—1492no—
218C2×C4—1492no—
219C2×C4D4×D14911yescharacteristic
220C2×C4D4×D14911yescharacteristic
221C2×C4C23×D14911yescharacteristic
222C8—22no—
223C8—2981no—
224C8—1492no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—5961no—
229C22—5961no—
230C22—5961no—
231C22C2×D4×D14911yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—2982no—
236C4—2982no—
237C4—5961no—
238C4—5962no—
239C4#1801193212yes—
240C4#41×D14911yescharacteristic
241C4#1801195611yescharacteristic
242C2—81no—
243C2—11921no—
244C2#2375029311yescharacteristic
245C2C2×#1801193211yescharacteristic
246C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#461×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558721C22
hypercenter#461D149
hypocenterC149#3393
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23750349C2semidirect
2. #23750345C2semidirect
4. #23750004C2semidirect
5. #23749850C2semidirect
6. #23749845C2semidirect
7. #23749831C2semidirect
8. #23749749C2semidirect
9. #23749717C2semidirect
11. #461×C149C2semidirect
123. C149#3393semidirect
132. #461D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237503492
#237503452
#237500062
#237500042
#237498502
#237498452
#237498312
#237497492
#237497172
C4×#145587212
#461×C1492
#3393149